In this introductory Linear Algebra tutorial, Brett shows you how to solve a 3x3 system of equations with three variables using Gaussian Elimination also known as row reduction. You'll learn how to transcribe a system of equations into an augmented matrix as well as the rules you can apply to the augmented matrix to manipulate it into both row echelon (also known as triangular form) and reduced row echelon form. In the end, you will easily be able to read off the solution, aka the intersection point of the three planes, from the matrix.

The THREE RULES you can use to row reduce your matrix are:
1. You can swap any two rows
2. You can multiply any row by a constant (including positive, negative, and fractional numbers)
3. You can add any two rows together

*Remember you can combine the rules together in any row reduction, as needed :)

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Backsolving (algebra) method for 3x3 systems »    • Solve a system of equations with thre...  
Elimination Method »    • ELIMINATION METHOD » how to solve sys...  
Substitution Method »    • SUBSTITUTION METHOD »  how to solve s...  

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